This randomized phase II trial studies how well bortezomib works when given after combination chemotherapy, rituximab, and an autologous stem cell transplant in treating patients with mantle cell lymphoma. Bortezomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) together with an autologous stem cell transplant may allow more chemotherapy to be given so that more cancer cells are killed. Monoclonal antibodies, such as rituximab, can block cancer growth in different ways. Some block the ability of cancer cells to grow and spread. Others find cancer cells and help kill them or carry cancer-killing substances to them. Giving bortezomib after combination chemotherapy, monoclonal antibody therapy, and an autologous stem cell transplant may kill any remaining cancer cells or keep the cancer from coming back.